In an arithmetic Progression the 7th term is 36 and the 15th term is 92 find the AP

Answer 1

In AP:

a = initial term a

d = common difference

an = a + ( n - 1 ) d

a7 = a + 6 d = 36

a15 = a + 14 d = 92

Now solve this system.

a + 6 d = 36
-
a + 14 d = 92
___________
- 8 d = - 56

d = - 56 / - 8 = 7

a + 6 d = 36

a + 6 ∙ 7 = 36

a + 42 = 36

a = 36 - 42

a = - 6

Your AP:

an = a + ( n - 1 ) d

an = - 6 + ( n - 1 ) ∙ 7

an = - 6 + 7 ( n - 1 )